Linearizable and nonlinearizable solutions in the nonlinear eigenvalue problem arising in the theory of electrodynamic waveguides filled with a nonlinear medium

In this paper, we consider a nonlinear eigenvalue problem on a segment, which describes the propagation of monochromatic (polarized) electromagnetic TM waves in a planar dielectric waveguide filled with a nonlinear medium. Results on the solvability of the problem and properties of the eigenvalues are obtained.